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This study investigates the effects of basalt–polypropylene fibers on the compressive strength and splitting tensile strength of concrete and calculates the fractal dimension of the pore structure of concrete by using a fractal model based on the optical method. Test results reveal that hybrid fibers can improve the compressive strength and splitting tensile strength of concrete, and the synergistic effect of the hybrid fibers is strongest when the contents of basalt fiber (BF) and polypropylene fiber (PF) are 0.05% each, and that the maximum increments in compressive strength and splitting tensile strength are 5.06% and 9.56%, respectively. The effect of hybrid fibers on splitting tensile strength is greater than on compressive strength. However, hybrid fibers have adverse effects on mechanical properties when the fiber content is too high. The pore structure of basalt–polypropylene fiber-reinforced concrete (BPFRC) exhibits obvious fractal characteristics, and the fractal dimension is calculated to be in the range of 2.297–2.482. The fractal dimension has a strong correlation with the air content and spacing factor: the air content decreases significantly whereas the spacing factor increases with increasing fractal dimension. In addition, the fractal dimension also has a strong positive correlation with compressive strength and splitting tensile strength. Therefore, the fractal dimension of the pore structure can be used to evaluate the microscopic pore structure of concrete and can also reflect the influence of the complexity of the pore structure on the macroscopic mechanical properties of concrete.